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Chapel: Heat Transfer (+ X10/Fortress)

Chapel: Heat Transfer (+ X10/Fortress). Brad Chamberlain Cray Inc. CSEP 524 May 20, 2010. Heat Transfer in Pictures. n. A:. repeat until max change < . n. 1.0. .  4. Heat Transfer in Chapel. config const n = 6, epsilon = 1.0e-5; const BigD : domain (2) = [0..n+1, 0..n+1],

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Chapel: Heat Transfer (+ X10/Fortress)

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  1. Chapel: Heat Transfer(+ X10/Fortress) Brad Chamberlain Cray Inc. CSEP 524 May 20, 2010

  2. Heat Transfer in Pictures n A: repeat until max change <  n 1.0   4

  3. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);

  4. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4.0; const delta = max reduce abs(A(D) - Temp(D)); A[D] = Temp[D]; } while (delta > epsilon); writeln(A); Declare program parameters const  can’t change values after initialization config can be set on executable command-line prompt> jacobi --n=10000 --epsilon=0.0001 note that no types are given; inferred from initializer n  integer (current default, 32 bits) epsilon  floating-point (current default, 64 bits)

  5. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; var delta = max reduce abs(A(D) - Temp(D)); A(D) = Temp(D); } while (delta > epsilon); writeln(A); Declare domains (first class index sets) domain(2) 2D arithmetic domain, indices are integer 2-tuples subdomain(P) a domain of the same type as P whose indices are guaranteed to be a subset of P’s exterior one of several built-in domain generators 0 n+1 0 n+1 BigD D LastRow

  6. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; var delta = max reduce abs(A(D) - Temp(D)); A(D) = Temp(D); } while (delta > epsilon); writeln(A); Declare arrays var can be modified throughout its lifetime : T declares variable to be of type T : [D] T array of size D with elements of type T (no initializer) values initialized to default value (0.0 for reals) BigD A Temp

  7. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; var delta = max reduce abs(A(D) - Temp(D)); A(D) = Temp(D); } while (delta > epsilon); writeln(A); Set Explicit Boundary Condition indexing by domain  slicing mechanism array expressions  parallel evaluation A

  8. Heat Transfer in Chapel Compute 5-point stencil [(i,j) in D] parallel forall expression over D’s indices, binding them to new variables i and j Note: since (i,j)  D and D BigDand Temp: [BigD]  no bounds check required for Temp(i,j) with compiler analysis, same can be proven for A’s accesses configconst n = 6, configconstepsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);   4

  9. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A); Compute maximum change op reduce  collapse aggregate expression to scalar using op Promotion:abs() and – are scalar operators, automatically promoted to work with array operands

  10. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A); Copy data back & Repeat until done uses slicing and whole array assignment standard do…while loop construct

  11. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1], D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A); Write array to console If written to a file, parallel I/O would be used

  12. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmapped Block, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4.0; var delta = max reduce abs(A(D) - Temp(D)); [ij in D] A(ij) = Temp(ij); } while (delta > epsilon); writeln(A); With this change, same code runs in a distributed manner Domain distribution maps indices to locales  decomposition of arrays & default location of iterations over locales Subdomains inherit parent domain’s distribution BigD D LastRow A Temp

  13. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmapped Block, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);

  14. Heat Transfer in Chapel(Variations)

  15. Heat Transfer in Chapel (double buffered version) configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmappedBlock, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); varA : [1..2] [BigD] real; A[..][LastRow] = 1.0; varsrc = 1, dst = 2; do { [(i,j) in D] A(dst)(i,j) = (A(src)(i-1,j) + A(src)(i+1,j) + A(src)(i,j-1) + A(src)(i,j+1)) / 4; const delta = max reduce abs(A[src] - A[dst]); src<=> dst; } while (delta > epsilon); writeln(A);

  16. Heat Transfer in Chapel (ZPL style) configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmappedBlock, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); const north = (-1,0), south = (1,0), east = (0,1), west = (0,-1); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [indin D] Temp(ind) = (A(ind + north) + A(ind + south) + A(ind + east) + A(ind + west)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);

  17. Heat Transfer in Chapel (array of offsets version) configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmappedBlock, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); param offset : [1..4] (int, int) = ((-1,0), (1,0), (0,1), (0,-1)); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [indin D] Temp(ind) = (+ reduce [off in offset] A(ind + off)) / offset.numElements; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);

  18. Heat Transfer in Chapel (sparse offsets version) configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmappedBlock, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); paramstencilSpace: domain(2) = [-1..1, -1..1], offSet: sparse subdomain(stencilSpace) = ((-1,0), (1,0), (0,1), (0,-1)); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [indin D] Temp(ind) = (+ reduce [off in offSet] A(ind + off)) / offSet.numIndices; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);

  19. The Other HPCS Languages

  20. X10 in a Nutshell • Heavily influenced by Java, Scala • emphasis on type safety, OOP design, small core language • also ZPL: support for global-view domains and arrays • Similar concepts to what you’ve heard about today in Chapel • yet a fairly different syntax and design aesthetic • Main differences from Chapel • For more information: • http://x10-lang.org/ • http://sf.net/projects/x10 • http://dist.codehaus.org/ • http://dist.codehaus.org/x10/documentation/presentations/UWMay2010.pdf

  21. X10: Similarities to Chapel • PGAS memory model • plus, language concepts for referring to realms of locality • more dynamic (“post-SPMD”) execution model • one logical task executes main() • any task can create additional tasks--local or remote • global-view data structures • ability to declare and access distributed arrays holistically rather than piecemeal • many similar concepts, often with different names/semantics • tasks vs. tasks • places vs. locales • ‘at’ vs. ‘on’ • ‘ateach’ vs’ ‘coforall’ + ‘on’ • ‘async’ vs. ‘begin’ • ‘finish’ vs. ‘sync’…

  22. X10: Differences from Chapel • X10: • takes a purer object-oriented approach • for example, arrays have reference rather than value semantics A = B; // alias or copy if A and B are arrays? • based on Java/Scala rather than ab initio • reflects IBM’s customer base relative to Cray’s • a bit more minimalist and purer • e.g., less likely to add abstractions to the language if expressible using objects • semantics distinguish between local and remote more strongly • e.g., communication is more visible in the code • e.g., some operations are not legal on remote objects • reflect differing choices on orthogonality vs. performance/safety • has a stronger story for exceptions

  23. Heat Transfer in X10 class HeatTransfer_v2 { constBigD = Dist.makeBlock([0..n+1, 0..n+1], 0); const D = BigD | ([1..n, 1..n] asRegion); const LR = [0..0, 1..n] as Region; const A = DistArray.make[double](BigD,(p:Point)=>{ LR.contains(p) ? 1 : 0 }); const Temp = DistArray.make[double](BigD); staticdef stencil_1((x,y):Point(2)) { return ((at(A.dist(x-1,y)) A(x-1,y)) + (at(A.dist(x+1,y)) A(x+1,y)) + A(x,y-1) + A(x,y+1)) / 4; } def run() { valD_Base = Dist.makeUnique(D.places()); vardelta:double = 1.0; do { finishateach (z inD_Base) for (p:Point(2) in D | here) Temp(p) = stencil_1(p); delta = A.lift(Temp, D.region, (x:double,y:double) =>Math.abs(x-y)).reduce(Math.max.(Double,Double), 0); finishateach (p in D) A(p) = Temp(p); } while (delta > epsilon); }

  24. Heat Transfer in Chapel configconst n = 6, epsilon = 1.0e-5; constBigD: domain(2) = [0..n+1, 0..n+1] dmapped Block, D: subdomain(BigD) = [1..n, 1..n], LastRow: subdomain(BigD) = D.exterior(1,0); var A, Temp : [BigD] real; A[LastRow] = 1.0; do { [(i,j) in D] Temp(i,j) = (A(i-1,j) + A(i+1,j) + A(i,j-1) + A(i,j+1)) / 4; const delta = max reduce abs(A[D] - Temp[D]); A[D] = Temp[D]; } while (delta > epsilon); writeln(A);

  25. Fortress in a Nutshell • The most blue-sky, clean-slate of the HPCS languages • Goal: define language semantics in libraries, not compiler: • data structures and types (including scalars types?) • operators, typecasts • operator precedence • in short, as much as possible to support future changes, languages • Other themes: • implicitly parallel -- most things are parallel by default • supports mathematical notation, symbols, operators • functional semantics • hierarchical representation of target architecture’s structure • units of measurement in the type system (meters, seconds, miles, …) • For more information: • http://research.sun.com/projects/plrg/ • http://projectfortress.sun.com/Projects/Community/

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